Answer: [tex]68^{\circ}[/tex]
Step-by-step explanation:
Assuming AC is a tangent, this means [tex]m\angle BAC=90^{\circ}[/tex].
Since arc BY measures 44 degrees, by the inscribed angle theorem, [tex]m\angle BAY=22^{\circ}[/tex].
This means [tex]m\angle YAC=90^{\circ}-22^{\circ}=68^{\circ}[/tex]
